penguins

Dados: palmerpenguins

# install.packages("palmerpenguins")
library(palmerpenguins)

skim(penguins)

Data summary

Name	penguins
Number of rows	344
Number of columns	8
_______________________
Column type frequency:
factor	3
numeric	5
________________________
Group variables	None

Variable type: factor

skim_variable	n_missing	complete_rate	ordered	n_unique	top_counts
species	0	1.00	FALSE	3	Ade: 152, Gen: 124, Chi: 68
island	0	1.00	FALSE	3	Bis: 168, Dre: 124, Tor: 52
sex	11	0.97	FALSE	2	mal: 168, fem: 165

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
bill_length_mm	2	0.99	43.92	5.46	32.1	39.23	44.45	48.5	59.6	▃▇▇▆▁
bill_depth_mm	2	0.99	17.15	1.97	13.1	15.60	17.30	18.7	21.5	▅▅▇▇▂
flipper_length_mm	2	0.99	200.92	14.06	172.0	190.00	197.00	213.0	231.0	▂▇▃▅▂
body_mass_g	2	0.99	4201.75	801.95	2700.0	3550.00	4050.00	4750.0	6300.0	▃▇▆▃▂
year	0	1.00	2008.03	0.82	2007.0	2007.00	2008.00	2009.0	2009.0	▇▁▇▁▇

Relação entre species e island

penguins %>%
  count(species, island) %>%
  mutate(species = as.character(species),
         island = as.character(island)) %>%
  tidyr::complete(species, island, fill = list(species = "Unknown", island = "Unknown")) %>%
  mutate(n = coalesce(n, 0L)) %>%
  ggplot(aes(y = n, x = island)) +
  geom_col() +
  facet_grid(~species) 

Variável resposta: Bill length

library(patchwork)
densidades <- penguins %>% 
  select(bill_length_mm, where(is.factor)) %>%
  pivot_longer(-bill_length_mm) %>%
  ggplot(aes(x = bill_length_mm)) +
  geom_density(aes(fill = value), alpha = 0.3) +
  facet_wrap(~name)

boxplots <- penguins %>% 
  select(bill_length_mm, where(is.factor)) %>%
  pivot_longer(-bill_length_mm) %>%
  ggplot(aes(x = bill_length_mm)) +
  geom_boxplot(aes(fill = value), alpha = 0.3, show.legend = FALSE) +
  facet_wrap(~name)
densidades/boxplots

p_species <- penguins %>% 
  select(bill_length_mm, species, where(is.numeric)) %>%
  pivot_longer(-c(bill_length_mm, species)) %>%
  ggplot(aes(x = value, y = bill_length_mm, colour = species)) +
  geom_point(alpha = 0.3, show.legend = FALSE) +
  geom_smooth(method = "lm", show.legend = FALSE) +
  facet_wrap(~name, scales = "free_x", ncol = 1)

p_island <- penguins %>% 
  select(bill_length_mm, island, where(is.numeric)) %>%
  pivot_longer(-c(bill_length_mm, island)) %>%
  ggplot(aes(x = value, y = bill_length_mm, colour = island)) +
  geom_point(alpha = 0.3, show.legend = FALSE) +
  geom_smooth(method = "lm", show.legend = FALSE) +
  facet_wrap(~name, scales = "free_x", ncol = 1)

p_sex <- penguins %>% 
  select(bill_length_mm, sex, where(is.numeric)) %>%
  pivot_longer(-c(bill_length_mm, sex)) %>%
  ggplot(aes(x = value, y = bill_length_mm, colour = sex)) +
  geom_point(alpha = 0.3, show.legend = FALSE) +
  geom_smooth(method = "lm", show.legend = FALSE) +
  facet_wrap(~name, scales = "free_x", ncol = 1)

p_species+p_island+p_sex

Modelagem

Passo 1) modelo full

mod1 <- lm(bill_length_mm ~ species*(. - island), data = penguins)

summary(mod1)

## 
## Call:
## lm(formula = bill_length_mm ~ species * (. - island), data = penguins)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.4330 -1.2819 -0.0174  1.2915 10.9968 
## 
## Coefficients:
##                                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                         1.391e+02  5.174e+02   0.269 0.788184    
## speciesChinstrap                   -6.957e+02  8.770e+02  -0.793 0.428173    
## speciesGentoo                      -9.199e+02  7.585e+02  -1.213 0.226098    
## bill_depth_mm                      -2.700e-02  2.036e-01  -0.133 0.894595    
## flipper_length_mm                   4.206e-02  3.478e-02   1.209 0.227526    
## body_mass_g                         1.130e-03  6.409e-04   1.763 0.078809 .  
## sexmale                             2.215e+00  5.690e-01   3.894 0.000121 ***
## year                               -5.632e-02  2.583e-01  -0.218 0.827528    
## speciesChinstrap:bill_depth_mm      8.948e-01  4.345e-01   2.059 0.040294 *  
## speciesGentoo:bill_depth_mm         5.462e-01  4.158e-01   1.314 0.189953    
## speciesChinstrap:flipper_length_mm -7.123e-02  6.934e-02  -1.027 0.305057    
## speciesGentoo:flipper_length_mm     8.064e-02  5.943e-02   1.357 0.175761    
## speciesChinstrap:body_mass_g        1.282e-04  1.176e-03   0.109 0.913274    
## speciesGentoo:body_mass_g           4.473e-04  9.823e-04   0.455 0.649188    
## speciesChinstrap:sexmale            5.810e-01  9.968e-01   0.583 0.560412    
## speciesGentoo:sexmale              -1.426e+00  9.570e-01  -1.491 0.137085    
## speciesChinstrap:year               3.497e-01  4.386e-01   0.797 0.425860    
## speciesGentoo:year                  4.475e-01  3.792e-01   1.180 0.238836    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.181 on 315 degrees of freedom
##   (11 observations deleted due to missingness)
## Multiple R-squared:  0.8491, Adjusted R-squared:  0.8409 
## F-statistic: 104.2 on 17 and 315 DF,  p-value: < 2.2e-16

vif(mod1)

##                                   GVIF Df GVIF^(1/(2*Df))
## species                   5.811539e+13  2     2761.040610
## bill_depth_mm             1.121734e+01  1        3.349230
## flipper_length_mm         1.658563e+01  1        4.072546
## body_mass_g               1.858269e+01  1        4.310764
## sex                       5.664629e+00  1        2.380048
## year                      3.077080e+00  1        1.754161
## species:bill_depth_mm     3.748106e+05  2       24.743034
## species:flipper_length_mm 4.416525e+06  2       45.842698
## species:body_mass_g       6.822424e+04  2       16.161612
## species:sex               5.273187e+01  2        2.694749
## species:year              5.913269e+13  2     2773.044986

plot(mod1)

Passo 2) retira variáveis com vif alto (species:year)

mod2 <- lm(bill_length_mm ~ species*(. - island - year) + year, data = penguins)

summary(mod2)

## 
## Call:
## lm(formula = bill_length_mm ~ species * (. - island - year) + 
##     year, data = penguins)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.2594 -1.2498 -0.0564  1.2760 10.9987 
## 
## Coefficients:
##                                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                        -3.398e+02  3.340e+02  -1.018 0.309671    
## speciesChinstrap                    4.076e+00  1.171e+01   0.348 0.728027    
## speciesGentoo                      -2.473e+01  1.078e+01  -2.293 0.022494 *  
## bill_depth_mm                       3.593e-02  1.967e-01   0.183 0.855204    
## flipper_length_mm                   2.824e-02  3.284e-02   0.860 0.390414    
## body_mass_g                         1.209e-03  6.370e-04   1.898 0.058565 .  
## sexmale                             2.135e+00  5.646e-01   3.780 0.000187 ***
## year                                1.828e-01  1.667e-01   1.097 0.273682    
## speciesChinstrap:bill_depth_mm      8.088e-01  4.225e-01   1.914 0.056502 .  
## speciesGentoo:bill_depth_mm         5.655e-01  4.099e-01   1.379 0.168753    
## speciesChinstrap:flipper_length_mm -4.843e-02  6.135e-02  -0.789 0.430493    
## speciesGentoo:flipper_length_mm     1.000e-01  5.723e-02   1.748 0.081506 .  
## speciesChinstrap:body_mass_g        3.968e-06  1.163e-03   0.003 0.997280    
## speciesGentoo:body_mass_g           3.294e-04  9.768e-04   0.337 0.736160    
## speciesChinstrap:sexmale            6.454e-01  9.941e-01   0.649 0.516703    
## speciesGentoo:sexmale              -1.486e+00  9.489e-01  -1.566 0.118343    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.18 on 317 degrees of freedom
##   (11 observations deleted due to missingness)
## Multiple R-squared:  0.8483, Adjusted R-squared:  0.8412 
## F-statistic: 118.2 on 15 and 317 DF,  p-value: < 2.2e-16

vif(mod2)

##                                   GVIF Df GVIF^(1/(2*Df))
## species                   2.274004e+06  2       38.832719
## bill_depth_mm             1.048870e+01  1        3.238626
## flipper_length_mm         1.480705e+01  1        3.847993
## body_mass_g               1.838961e+01  1        4.288310
## sex                       5.586635e+00  1        2.363606
## year                      1.283735e+00  1        1.133020
## species:bill_depth_mm     3.474193e+05  2       24.278032
## species:flipper_length_mm 3.254653e+06  2       42.474296
## species:body_mass_g       6.626416e+04  2       16.044260
## species:sex               5.132434e+01  2        2.676584

plot(mod2)

Passo 3) retira variáveis com vif alto (year)

mod3 <- lm(bill_length_mm ~ species*(. - island - year - flipper_length_mm) + year + flipper_length_mm, data = penguins)

summary(mod3)

## 
## Call:
## lm(formula = bill_length_mm ~ species * (. - island - year - 
##     flipper_length_mm) + year + flipper_length_mm, data = penguins)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.3335 -1.3068 -0.1156  1.2718 11.7595 
## 
## Coefficients:
##                                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                    -2.487e+02  3.327e+02  -0.747 0.455341    
## speciesChinstrap               -2.979e+00  7.129e+00  -0.418 0.676319    
## speciesGentoo                  -9.595e+00  6.205e+00  -1.546 0.123018    
## bill_depth_mm                   1.889e-02  1.973e-01   0.096 0.923811    
## body_mass_g                     1.106e-03  6.268e-04   1.764 0.078680 .  
## sexmale                         2.150e+00  5.670e-01   3.791 0.000179 ***
## year                            1.361e-01  1.660e-01   0.820 0.412953    
## flipper_length_mm               4.547e-02  2.526e-02   1.800 0.072730 .  
## speciesChinstrap:bill_depth_mm  7.592e-01  4.218e-01   1.800 0.072818 .  
## speciesGentoo:bill_depth_mm     8.111e-01  3.938e-01   2.060 0.040244 *  
## speciesChinstrap:body_mass_g   -3.969e-04  1.076e-03  -0.369 0.712547    
## speciesGentoo:body_mass_g       8.189e-04  9.360e-04   0.875 0.382295    
## speciesChinstrap:sexmale        4.120e-01  9.841e-01   0.419 0.675715    
## speciesGentoo:sexmale          -1.419e+00  9.522e-01  -1.490 0.137192    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.189 on 319 degrees of freedom
##   (11 observations deleted due to missingness)
## Multiple R-squared:  0.846,  Adjusted R-squared:  0.8398 
## F-statistic: 134.8 on 13 and 319 DF,  p-value: < 2.2e-16

vif(mod3)

##                               GVIF Df GVIF^(1/(2*Df))
## species               2.771118e+05  2       22.943716
## bill_depth_mm         1.046371e+01  1        3.234766
## body_mass_g           1.764682e+01  1        4.200811
## sex                   5.585729e+00  1        2.363415
## year                  1.262277e+00  1        1.123511
## flipper_length_mm     8.682095e+00  1        2.946539
## species:bill_depth_mm 3.115446e+05  2       23.625448
## species:body_mass_g   5.071528e+04  2       15.006683
## species:sex           4.955123e+01  2        2.653161

plot(mod3)

Passo 4) vif alto (bill_depth_mm)

mod4 <- lm(bill_length_mm ~ . + species*sex, data = penguins)

summary(mod4)

## 
## Call:
## lm(formula = bill_length_mm ~ . + species * sex, data = penguins)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.0597 -1.3195  0.0233  1.2233 11.8454 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              -4.332e+02  3.250e+02  -1.333  0.18352    
## speciesChinstrap          9.209e+00  5.270e-01  17.476  < 2e-16 ***
## speciesGentoo             6.191e+00  1.132e+00   5.471 9.02e-08 ***
## islandDream              -4.444e-01  4.492e-01  -0.989  0.32329    
## islandTorgersen          -4.514e-02  4.696e-01  -0.096  0.92347    
## bill_depth_mm             3.043e-01  1.559e-01   1.952  0.05185 .  
## flipper_length_mm         4.675e-02  2.574e-02   1.816  0.07027 .  
## body_mass_g               1.371e-03  4.394e-04   3.121  0.00197 ** 
## sexmale                   1.556e+00  4.750e-01   3.276  0.00117 ** 
## year                      2.250e-01  1.625e-01   1.385  0.16707    
## speciesChinstrap:sexmale  1.511e+00  6.712e-01   2.251  0.02504 *  
## speciesGentoo:sexmale     3.874e-01  5.547e-01   0.698  0.48546    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.207 on 321 degrees of freedom
##   (11 observations deleted due to missingness)
## Multiple R-squared:  0.8425, Adjusted R-squared:  0.8371 
## F-statistic: 156.1 on 11 and 321 DF,  p-value: < 2.2e-16

vif(mod4)

##                        GVIF Df GVIF^(1/(2*Df))
## species           51.031073  2        2.672752
## island             3.762136  2        1.392703
## bill_depth_mm      6.427030  1        2.535159
## flipper_length_mm  8.873659  1        2.978869
## body_mass_g        8.532496  1        2.921044
## sex                3.855616  1        1.963572
## year               1.189720  1        1.090743
## species:sex        7.466449  2        1.653022

plot(mod4)

Passo 5) retirando potencial ponto de alavanca (294)

mod5 <- lm(bill_length_mm ~ . + species*sex, data = penguins[-294,])

summary(mod5)

## 
## Call:
## lm(formula = bill_length_mm ~ . + species * sex, data = penguins[-294, 
##     ])
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -7.019 -1.288  0.080  1.234  8.801 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              -4.666e+02  3.099e+02  -1.506 0.133162    
## speciesChinstrap          8.806e+00  5.071e-01  17.364  < 2e-16 ***
## speciesGentoo             5.923e+00  1.080e+00   5.486 8.37e-08 ***
## islandDream              -4.652e-01  4.282e-01  -1.086 0.278130    
## islandTorgersen          -8.591e-02  4.477e-01  -0.192 0.847928    
## bill_depth_mm             2.866e-01  1.487e-01   1.928 0.054784 .  
## flipper_length_mm         6.300e-02  2.470e-02   2.551 0.011215 *  
## body_mass_g               1.205e-03  4.198e-04   2.870 0.004378 ** 
## sexmale                   1.619e+00  4.529e-01   3.574 0.000405 ***
## year                      2.406e-01  1.549e-01   1.553 0.121469    
## speciesChinstrap:sexmale  1.779e+00  6.415e-01   2.774 0.005869 ** 
## speciesGentoo:sexmale     3.414e-01  5.288e-01   0.646 0.518996    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.104 on 320 degrees of freedom
##   (11 observations deleted due to missingness)
## Multiple R-squared:  0.8545, Adjusted R-squared:  0.8495 
## F-statistic: 170.8 on 11 and 320 DF,  p-value: < 2.2e-16

plot(mod5)

Passo 6) Elimina um termo não significante (island)

mod6 <- lm(bill_length_mm ~ . + species*sex - island, data = penguins[-294,])

summary(mod6)

## 
## Call:
## lm(formula = bill_length_mm ~ . + species * sex - island, data = penguins[-294, 
##     ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.9133 -1.3140  0.0614  1.2481  8.7991 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              -4.830e+02  3.081e+02  -1.568 0.117974    
## speciesChinstrap          8.546e+00  4.535e-01  18.844  < 2e-16 ***
## speciesGentoo             6.186e+00  1.021e+00   6.058 3.85e-09 ***
## bill_depth_mm             2.996e-01  1.481e-01   2.023 0.043917 *  
## flipper_length_mm         6.203e-02  2.435e-02   2.547 0.011321 *  
## body_mass_g               1.209e-03  4.187e-04   2.888 0.004144 ** 
## sexmale                   1.596e+00  4.520e-01   3.532 0.000473 ***
## year                      2.486e-01  1.540e-01   1.614 0.107502    
## speciesChinstrap:sexmale  1.786e+00  6.407e-01   2.788 0.005623 ** 
## speciesGentoo:sexmale     3.498e-01  5.282e-01   0.662 0.508282    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.102 on 322 degrees of freedom
##   (11 observations deleted due to missingness)
## Multiple R-squared:  0.8539, Adjusted R-squared:  0.8498 
## F-statistic:   209 on 9 and 322 DF,  p-value: < 2.2e-16

mod6 %>%
  augment() %>%
  ggplot(aes(x = flipper_length_mm, colour = species, shape = sex)) +
  geom_point(aes(y = bill_length_mm), show.legend = FALSE) +
  geom_line(aes(y = .fitted), show.legend = FALSE)

Passo 7) Elimina termos não significantes

mod7 <- lm(bill_length_mm ~ . + species*sex - island - year, data = penguins[-294,])

summary(mod7)

## 
## Call:
## lm(formula = bill_length_mm ~ . + species * sex - island - year, 
##     data = penguins[-294, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.1685 -1.2449  0.0171  1.2065  8.4895 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              1.428e+01  4.257e+00   3.354 0.000891 ***
## speciesChinstrap         8.478e+00  4.527e-01  18.729  < 2e-16 ***
## speciesGentoo            5.805e+00  9.960e-01   5.828 1.36e-08 ***
## bill_depth_mm            2.677e-01  1.471e-01   1.819 0.069824 .  
## flipper_length_mm        7.681e-02  2.262e-02   3.395 0.000772 ***
## body_mass_g              1.139e-03  4.175e-04   2.729 0.006703 ** 
## sexmale                  1.621e+00  4.528e-01   3.580 0.000396 ***
## speciesChinstrap:sexmale 1.720e+00  6.410e-01   2.684 0.007661 ** 
## speciesGentoo:sexmale    2.967e-01  5.285e-01   0.561 0.574916    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.107 on 323 degrees of freedom
##   (11 observations deleted due to missingness)
## Multiple R-squared:  0.8527, Adjusted R-squared:  0.849 
## F-statistic: 233.7 on 8 and 323 DF,  p-value: < 2.2e-16

mod7 %>%
  augment() %>%
  ggplot(aes(x = flipper_length_mm, colour = species, shape = sex)) +
  geom_point(aes(y = bill_length_mm), show.legend = FALSE) +
  geom_line(aes(y = .fitted), show.legend = FALSE)

lista_de_modelos <- list(
  mod1,
  mod2,
  mod3,
  mod4,
  mod5,
  mod6,
  mod7
)
modelsummary::modelsummary(lista_de_modelos)

	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6	Model 7
(Intercept)	139.130	−339.833	−248.663	−433.227	−466.555	−482.973	14.279
	(517.407)	(333.974)	(332.681)	(325.035)	(309.884)	(308.112)	(4.257)
speciesChinstrap	−695.731	4.076	−2.979	9.209	8.806	8.546	8.478
	(876.957)	(11.712)	(7.129)	(0.527)	(0.507)	(0.453)	(0.453)
speciesGentoo	−919.910	−24.731	−9.595	6.191	5.923	6.186	5.805
	(758.473)	(10.785)	(6.205)	(1.132)	(1.080)	(1.021)	(0.996)
bill_depth_mm	−0.027	0.036	0.019	0.304	0.287	0.300	0.268
	(0.204)	(0.197)	(0.197)	(0.156)	(0.149)	(0.148)	(0.147)
flipper_length_mm	0.042	0.028	0.045	0.047	0.063	0.062	0.077
	(0.035)	(0.033)	(0.025)	(0.026)	(0.025)	(0.024)	(0.023)
body_mass_g	0.001	0.001	0.001	0.001	0.001	0.001	0.001
	(0.001)	(0.001)	(0.001)	(0.000)	(0.000)	(0.000)	(0.000)
sexmale	2.215	2.135	2.150	1.556	1.619	1.596	1.621
	(0.569)	(0.565)	(0.567)	(0.475)	(0.453)	(0.452)	(0.453)
year	−0.056	0.183	0.136	0.225	0.241	0.249
	(0.258)	(0.167)	(0.166)	(0.163)	(0.155)	(0.154)
speciesChinstrap × bill_depth_mm	0.895	0.809	0.759
	(0.435)	(0.423)	(0.422)
speciesGentoo × bill_depth_mm	0.546	0.565	0.811
	(0.416)	(0.410)	(0.394)
speciesChinstrap × flipper_length_mm	−0.071	−0.048
	(0.069)	(0.061)
speciesGentoo × flipper_length_mm	0.081	0.100
	(0.059)	(0.057)
speciesChinstrap × body_mass_g	0.000	0.000	0.000
	(0.001)	(0.001)	(0.001)
speciesGentoo × body_mass_g	0.000	0.000	0.001
	(0.001)	(0.001)	(0.001)
speciesChinstrap × sexmale	0.581	0.645	0.412	1.511	1.779	1.786	1.720
	(0.997)	(0.994)	(0.984)	(0.671)	(0.642)	(0.641)	(0.641)
speciesGentoo × sexmale	−1.426	−1.486	−1.419	0.387	0.341	0.350	0.297
	(0.957)	(0.949)	(0.952)	(0.555)	(0.529)	(0.528)	(0.528)
speciesChinstrap × year	0.350
	(0.439)
speciesGentoo × year	0.447
	(0.379)
islandDream				−0.444	−0.465
				(0.449)	(0.428)
islandTorgersen				−0.045	−0.086
				(0.470)	(0.448)
Num.Obs.	333	333	333	333	332	332	332
R2	0.849	0.848	0.846	0.843	0.854	0.854	0.853
R2 Adj.	0.841	0.841	0.840	0.837	0.849	0.850	0.849
AIC	1483.9	1481.5	1482.5	1486.0	1449.8	1447.2	1447.9
BIC	1556.3	1546.2	1539.6	1535.5	1499.2	1489.1	1485.9
Log.Lik.	−722.948	−723.748	−726.250	−729.994	−711.877	−712.601	−713.939
F	104.235	118.212	134.846	156.148	170.833	209.030	233.672
RMSE	2.18	2.18	2.19	2.21	2.10	2.10	2.11

modelsummary::modelplot(lista_de_modelos[5:7], coef_omit = "Intercept")

library(gtsummary)

tbl_regression(mod7)

Characteristic	Beta	95% CI1	p-value
species
Adelie	—	—
Chinstrap	8.5	7.6, 9.4	<0.001
Gentoo	5.8	3.8, 7.8	<0.001
bill_depth_mm	0.27	-0.02, 0.56	0.070
flipper_length_mm	0.08	0.03, 0.12	<0.001
body_mass_g	0.00	0.00, 0.00	0.007
sex
female	—	—
male	1.6	0.73, 2.5	<0.001
species * sex
Chinstrap * male	1.7	0.46, 3.0	0.008
Gentoo * male	0.30	-0.74, 1.3	0.6
1 CI = Confidence Interval